Title: The extensions of $C^*$-algebras with tracial topological rank no more than one
Abstract: I → A → A/I → 0 be a short exact sequence of C * -algebras with A unital.Suppose that I has tracial topological rank no more than one and A/I is TAI (in particular, if A/I is simple and has tracial topological rank no more than one).It will be proved that A has tracial topological rank no more than one if the extension is quasidiagonal, and A has the property (P1) if the extension is tracially quasidiagonal.